Detecting Facial Landmarks on 3D Models Based on Geometric Properties—A Review of Algorithms, Enhancements, Additions and Open-Source Implementations

Facial landmark detection, a crucial aspect of face recognition, is widely used in various fields, such as facial surgeries, biometrics, and surveillance systems. With the advancement of affordable and capable 3D scanning technologies, research on automatically detecting facial landmarks on 3D models is gaining momentum. Utilizing the geometric properties of 3D facial models, researchers have developed algorithms for various landmarks with varying levels of accuracy. In this study, we reviewed existing literature and developed algorithms for thirty-eight landmarks using geometric properties and statistical information about facial measurements. The algorithms for thirty landmarks are original contributions to the literature. We provide the implementation of all the algorithms as open-source Python code, along with the pseudocode for both our algorithms and those found in the literature. To the best of our knowledge, this study covers the largest number of facial landmark detection algorithms based on the geometric properties of 3D models. This is the first study that provides the implementation of the algorithms along with detailed pseudocode. The results of the algorithms are presented by calculating the mean, median, standard deviation, minimum, and maximum of the errors and depicting the histogram for each landmark over a hundred 3D facial scans. The results show that geometric properties and statistics can be utilized to achieve more robust solutions for facial landmark detection.